%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:27:12 PM UTC 2026
% Result : Unsatisfiable 0.14s 1.03s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 3
% Syntax : Number of clauses : 76 ( 76 unt; 0 nHn; 3 RR)
% Number of literals : 76 ( 75 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 282 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t1,axiom,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X3))),double_divide(X4,double_divide(X2,X4))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t2,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X3))),double_divide(X4,double_divide(X2,X4))))) = X3,
inference(orient,[status(thm)],[t1]) ).
cnf(t1724,plain,
double_divide(inverse(X1),multiply(double_divide(X4,double_divide(X2,X4)),inverse(double_divide(X1,double_divide(X2,X3))))) = X3,
inference(step,[status(thm)],[t2,t5]) ).
cnf(t1725,plain,
double_divide(inverse(X1),multiply(double_divide(X4,double_divide(X2,X4)),multiply(double_divide(X2,X3),X1))) = X3,
inference(step,[status(thm)],[t1724,t5]) ).
cnf(t6,plain,
double_divide(inverse(X1),multiply(double_divide(X4,double_divide(X2,X4)),multiply(double_divide(X2,X3),X1))) = X3,
inference(rw,[status(thm)],[t1725]) ).
cnf(t7,plain,
double_divide(inverse(X1),multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),X1))) = X4,
inference(orient,[status(thm)],[t6]) ).
cnf(t8,plain,
X1 = double_divide(multiply(X2,X3),multiply(double_divide(X4,double_divide(Y4,X4)),multiply(double_divide(Y4,X1),double_divide(X3,X2)))),
inference(cp,[status(thm)],[t7,t5]) ).
cnf(t16,plain,
double_divide(multiply(X1,X2),multiply(double_divide(X3,double_divide(X4,X3)),multiply(double_divide(X4,Y4),double_divide(X2,X1)))) = Y4,
inference(orient,[status(thm)],[t8]) ).
cnf(t11,plain,
multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X4)) = double_divide(inverse(Y4),multiply(double_divide(Y5,double_divide(inverse(X4),Y5)),multiply(X3,Y4))),
inference(cp,[status(thm)],[t7,t7]) ).
cnf(t65,plain,
multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X4)) = double_divide(inverse(Y4),multiply(double_divide(Y5,double_divide(inverse(X4),Y5)),multiply(X3,Y4))),
inference(orient,[status(thm)],[t11]) ).
cnf(t77,plain,
X1 = double_divide(multiply(X2,X3),double_divide(inverse(X4),multiply(double_divide(Y4,double_divide(inverse(double_divide(X3,X2)),Y4)),multiply(X1,X4)))),
inference(cp,[status(thm)],[t16,t65]) ).
cnf(t1727,plain,
X1 = double_divide(multiply(X2,X3),double_divide(inverse(X4),multiply(double_divide(Y4,double_divide(multiply(X2,X3),Y4)),multiply(X1,X4)))),
inference(step,[status(thm)],[t77,t5]) ).
cnf(t211,plain,
double_divide(multiply(X1,X2),double_divide(inverse(X3),multiply(double_divide(X4,double_divide(multiply(X1,X2),X4)),multiply(Y4,X3)))) = Y4,
inference(orient,[status(thm)],[t1727]) ).
cnf(t90,plain,
multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,double_divide(inverse(X3),X4)),X3)) = X4,
inference(cp,[status(thm)],[t65,t7]) ).
cnf(t119,plain,
multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,double_divide(inverse(X3),X4)),X3)) = X4,
inference(orient,[status(thm)],[t90]) ).
cnf(t212,plain,
X1 = double_divide(X2,double_divide(inverse(X3),multiply(double_divide(X4,double_divide(multiply(double_divide(Y4,double_divide(Y5,Y4)),multiply(double_divide(Y5,double_divide(inverse(Y6),X2)),Y6)),X4)),multiply(X1,X3)))),
inference(cp,[status(thm)],[t211,t119]) ).
cnf(t1731,plain,
X1 = double_divide(X2,double_divide(inverse(X3),multiply(double_divide(X4,double_divide(X2,X4)),multiply(X1,X3)))),
inference(step,[status(thm)],[t212,t119]) ).
cnf(t621,plain,
double_divide(X1,double_divide(inverse(X2),multiply(double_divide(X3,double_divide(X1,X3)),multiply(X4,X2)))) = X4,
inference(orient,[status(thm)],[t1731]) ).
cnf(t228,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(multiply(X3,X4),double_divide(inverse(multiply(double_divide(X2,double_divide(inverse(Y4),Y5)),Y4)),multiply(double_divide(Y6,double_divide(multiply(X3,X4),Y6)),Y5))),
inference(cp,[status(thm)],[t211,t119]) ).
cnf(t128,plain,
double_divide(X1,X2) = double_divide(inverse(multiply(double_divide(X1,double_divide(inverse(X3),X4)),X3)),multiply(double_divide(Y4,double_divide(X2,Y4)),X4)),
inference(cp,[status(thm)],[t7,t119]) ).
cnf(t158,plain,
double_divide(inverse(multiply(double_divide(X1,double_divide(inverse(X2),X3)),X2)),multiply(double_divide(X4,double_divide(Y4,X4)),X3)) = double_divide(X1,Y4),
inference(orient,[status(thm)],[t128]) ).
cnf(t1728,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(multiply(X3,X4),double_divide(X2,multiply(X3,X4))),
inference(step,[status(thm)],[t228,t158]) ).
cnf(t261,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(multiply(X3,X4),double_divide(X2,multiply(X3,X4))),
inference(orient,[status(thm)],[t1728]) ).
cnf(t309,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,multiply(double_divide(X4,double_divide(Y4,X4)),multiply(double_divide(Y4,double_divide(inverse(Y5),X3)),Y5)))),
inference(cp,[status(thm)],[t261,t119]) ).
cnf(t1729,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(step,[status(thm)],[t309,t119]) ).
cnf(t358,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(orient,[status(thm)],[t1729]) ).
cnf(t377,plain,
X1 = multiply(double_divide(X2,double_divide(X1,X2)),multiply(double_divide(X3,double_divide(inverse(X4),X3)),X4)),
inference(cp,[status(thm)],[t119,t358]) ).
cnf(t683,plain,
multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X3,double_divide(inverse(X4),X3)),X4)) = X2,
inference(orient,[status(thm)],[t377]) ).
cnf(t365,plain,
multiply(double_divide(X1,X2),X2) = inverse(double_divide(X3,double_divide(X1,X3))),
inference(cp,[status(thm)],[t5,t358]) ).
cnf(t1730,plain,
multiply(double_divide(X1,X2),X2) = multiply(double_divide(X1,X3),X3),
inference(step,[status(thm)],[t365,t5]) ).
cnf(t403,plain,
multiply(double_divide(X1,X2),X2) = multiply(double_divide(X1,X3),X3),
inference(orient,[status(thm)],[t1730]) ).
cnf(t411,plain,
X1 = double_divide(inverse(X1),multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),X4))),
inference(cp,[status(thm)],[t7,t403]) ).
cnf(t723,plain,
double_divide(inverse(X1),multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),X4))) = X1,
inference(orient,[status(thm)],[t411]) ).
cnf(t724,plain,
multiply(double_divide(X1,double_divide(inverse(X2),multiply(double_divide(X3,X4),X4))),X2) = double_divide(X1,X3),
inference(cp,[status(thm)],[t723,t158]) ).
cnf(t788,plain,
multiply(double_divide(X1,double_divide(inverse(X2),multiply(double_divide(X3,X4),X4))),X2) = double_divide(X1,X3),
inference(orient,[status(thm)],[t724]) ).
cnf(t813,plain,
X1 = multiply(double_divide(X2,double_divide(X1,X2)),double_divide(multiply(double_divide(X3,X4),X4),X3)),
inference(cp,[status(thm)],[t683,t788]) ).
cnf(t830,plain,
multiply(double_divide(X1,double_divide(X2,X1)),double_divide(multiply(double_divide(X3,X4),X4),X3)) = X2,
inference(orient,[status(thm)],[t813]) ).
cnf(t863,plain,
X1 = multiply(double_divide(X2,double_divide(X1,X2)),inverse(double_divide(multiply(double_divide(X3,X4),X4),X3))),
inference(cp,[status(thm)],[t119,t830]) ).
cnf(t1732,plain,
X1 = multiply(double_divide(X2,double_divide(X1,X2)),multiply(X3,multiply(double_divide(X3,X4),X4))),
inference(step,[status(thm)],[t863,t5]) ).
cnf(t878,plain,
multiply(double_divide(X1,double_divide(X2,X1)),multiply(X3,multiply(double_divide(X3,X4),X4))) = X2,
inference(orient,[status(thm)],[t1732]) ).
cnf(t911,plain,
X1 = double_divide(X2,double_divide(inverse(multiply(double_divide(X1,X3),X3)),X2)),
inference(cp,[status(thm)],[t621,t878]) ).
cnf(t996,plain,
double_divide(X1,double_divide(inverse(multiply(double_divide(X2,X3),X3)),X1)) = X2,
inference(orient,[status(thm)],[t911]) ).
cnf(t1017,plain,
multiply(double_divide(inverse(multiply(double_divide(X1,X2),X2)),X3),X3) = inverse(X1),
inference(cp,[status(thm)],[t5,t996]) ).
cnf(t1421,plain,
multiply(double_divide(inverse(multiply(double_divide(X1,X2),X2)),X3),X3) = inverse(X1),
inference(orient,[status(thm)],[t1017]) ).
cnf(t1452,plain,
X1 = double_divide(inverse(X1),multiply(double_divide(X2,double_divide(inverse(multiply(double_divide(X3,X4),X4)),X2)),inverse(X3))),
inference(cp,[status(thm)],[t7,t1421]) ).
cnf(t1734,plain,
X1 = double_divide(inverse(X1),multiply(X3,inverse(X3))),
inference(step,[status(thm)],[t1452,t996]) ).
cnf(t1474,plain,
double_divide(inverse(X1),multiply(X2,inverse(X2))) = X1,
inference(orient,[status(thm)],[t1734]) ).
cnf(t9,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X4)),inverse(X4)) = inverse(X3),
inference(cp,[status(thm)],[t5,t7]) ).
cnf(t12,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X4)),inverse(X4)) = inverse(X3),
inference(orient,[status(thm)],[t9]) ).
cnf(t131,plain,
inverse(double_divide(X1,X2)) = multiply(multiply(double_divide(X3,double_divide(X2,X3)),X4),inverse(multiply(double_divide(X1,double_divide(inverse(Y4),X4)),Y4))),
inference(cp,[status(thm)],[t12,t119]) ).
cnf(t1726,plain,
multiply(X2,X1) = multiply(multiply(double_divide(X3,double_divide(X2,X3)),X4),inverse(multiply(double_divide(X1,double_divide(inverse(Y4),X4)),Y4))),
inference(step,[status(thm)],[t131,t5]) ).
cnf(t196,plain,
multiply(multiply(double_divide(X1,double_divide(X2,X1)),X3),inverse(multiply(double_divide(X4,double_divide(inverse(Y4),X3)),Y4))) = multiply(X2,X4),
inference(orient,[status(thm)],[t1726]) ).
cnf(t1477,plain,
X1 = double_divide(inverse(X1),multiply(inverse(X2),X2)),
inference(cp,[status(thm)],[t1474,t196]) ).
cnf(t1533,plain,
double_divide(inverse(X1),multiply(inverse(X2),X2)) = X1,
inference(orient,[status(thm)],[t1477]) ).
cnf(t1001,plain,
X1 = double_divide(double_divide(inverse(X2),multiply(double_divide(X3,double_divide(inverse(multiply(double_divide(X1,X4),X4)),X3)),multiply(Y4,X2))),Y4),
inference(cp,[status(thm)],[t996,t621]) ).
cnf(t1733,plain,
X1 = double_divide(double_divide(inverse(X2),multiply(X1,multiply(Y4,X2))),Y4),
inference(step,[status(thm)],[t1001,t996]) ).
cnf(t1090,plain,
double_divide(double_divide(inverse(X1),multiply(X2,multiply(X3,X1))),X3) = X2,
inference(orient,[status(thm)],[t1733]) ).
cnf(t1543,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(cp,[status(thm)],[t1090,t1533]) ).
cnf(t1593,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t1543]) ).
cnf(t13,plain,
inverse(X1) = multiply(multiply(double_divide(multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),Y4)),X4),multiply(double_divide(inverse(Y4),X1),Y5)),inverse(Y5)),
inference(cp,[status(thm)],[t12,t7]) ).
cnf(t54,plain,
multiply(multiply(double_divide(multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X4)),X3),multiply(double_divide(inverse(X4),Y4),Y5)),inverse(Y5)) = inverse(Y4),
inference(orient,[status(thm)],[t13]) ).
cnf(t1601,plain,
double_divide(inverse(X1),multiply(double_divide(multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),Y4)),X4),multiply(double_divide(inverse(Y4),Y5),X1))) = inverse(inverse(Y5)),
inference(cp,[status(thm)],[t1593,t54]) ).
cnf(t10,plain,
X1 = double_divide(inverse(X2),multiply(double_divide(multiply(double_divide(X3,double_divide(X4,X3)),multiply(double_divide(X4,Y4),Y5)),Y4),multiply(double_divide(inverse(Y5),X1),X2))),
inference(cp,[status(thm)],[t7,t7]) ).
cnf(t32,plain,
double_divide(inverse(X1),multiply(double_divide(multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),Y4)),X4),multiply(double_divide(inverse(Y4),Y5),X1))) = Y5,
inference(orient,[status(thm)],[t10]) ).
cnf(t1744,plain,
Y5 = inverse(inverse(Y5)),
inference(step,[status(thm)],[t1601,t32]) ).
cnf(t1636,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t1744]) ).
cnf(t1637,plain,
inverse(X1) = double_divide(X1,multiply(inverse(X2),X2)),
inference(cp,[status(thm)],[t1533,t1636]) ).
cnf(t1655,plain,
double_divide(X1,multiply(inverse(X2),X2)) = inverse(X1),
inference(orient,[status(thm)],[t1637]) ).
cnf(t1660,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t5,t1655]) ).
cnf(t1745,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(step,[status(thm)],[t1660,t1636]) ).
cnf(t1709,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t1745]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a2 != a2,
inference(rw,[status(thm)],[goal_0,t1709]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.56 % Computer : n016.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.02/0.56 % CPULimit : 300
% 0.02/0.56 % WCLimit : 300
% 0.02/0.56 % DateTime : Wed Sep 23 15:00:00 UTC 2026
% 0.02/0.56 % CPUTime :
% 0.02/0.56 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/1.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/1.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------